The 46-year-old, who was former Delaware Attorney-General, was taken to hospital earlier this month at the Walter Reed Army Medical Centre, near Washington.
Beau Biden was seen as a rising star of U.S. politics but suffered health problems in recent years. He had intended to run for Delaware State governor in 2016.
In a statement on Sunday, President Barack Obama said: “Michelle and I are grieving tonight.
“Beau was a good, big-hearted, devoutly Catholic and deeply faithful man, who made a difference in the lives of all he touched, and he lives on in their hearts.”
Beau Biden was diagnosed with brain cancer in August 2013 and underwent treatment that was initially successful. However, the cancer recurred earlier this year.
Announcing the death in a statement, the Vice-President said: “It is with broken hearts that Hallie, Hunter, Ashley, Jill and I announce the passing of our husband, brother and son, Beau, after he battled brain cancer with the same integrity, courage and strength he demonstrated every day of his life.
“Beau embodied my father’s saying that a parent knows success when his child turns out better than he did,” he said, adding: “We know that Beau’s spirit will live on in all of us.”
According to a BBC report on Sunday, Beau Biden suffered a mild stroke in 2010. Three years later, he received surgery at a Texas cancer centre for what was said to be a small lesion.
The eldest of Biden’s two sons, he served a year-long tour Iraq in 2008 as a captain in the Delaware National Guard.
As a child, Beau survived a car crash that killed his mother Neilia and his baby sister Naomi in 1972. He and his brother, Hunter, were injured.
Joe Biden had just been elected to the Senate, and took his oath of office by his son’s hospital bed.
Joe Biden married Jill Jacobs in 1977. They have one daughter, Ashley Blazer.
Beau Biden is survived by his wife Hallie and their two children, Natalie and Hunter.
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